A Theory about Logical Theories of “Expressions of the Form ‘The So and So’, Where ‘The’ is in the Singular”

Abstract

In Meaning and Necessity, Carnap briefly and critically assessed the approaches to definite descriptions associated with the names of Frege, Russell and Hubert and Bernays.² Ultimately he adopted a version of the Frege approach, now widely known as the chosen object method, in the development of his influential doctrine of meaning and modality. Since Carnap’s discussion, however, another approach to definite descriptions, called free description theory, has emerged. Moreover, Carnap did not concern himself with the question whether there exists a way of understanding the various approaches to definite descriptions such that they can be construed as different options to a common technical problem. Such a way exists in set theory where various approaches can be construed as different options to the paradoxical axiom of set abstraction in naive set theory. That is the task of this essay; to provide a way of understanding both the traditional and free logic approaches to the treatment of definite descriptions such that they all can be seen as different ways out of a common technical problem, a problem manifested in what will be called The Naive Theory of Definite Descriptions.

The quoted expression in the title of this essay is the way Russell defined definite descriptions in Principia Mathematica. Thanks are due to Ermanno Bencivenga for his helpful comments.